THERMAL ANALYSIS OF CHARRING MATERIALS BASED ON PYROLYSIS INTERFACE MODEL

Transcription

1 THERMA SCIENCE, Year 14, Vol. 18, No. 5, THERMA ANAYSIS OF CHARRING MATERIAS BASED ON PYROYSIS INTERFACE MODE by Hai-Ming HUANG *a, Wei-Jie I a, and Hai-ingYU b a Institute of Engineering Mechanics, Beiing Jiaotong University, Beiing, China b Sichuan Academy of Aerosace Technology, Chengdu, China Original scientific aer DOI: 1.98/TSCI145591H Charring thermal rotection systems have been used to rotect hyersonic vehicles from high heat loads. The yrolysis of charring materials is a comlicated hysical and chemical henomenon. Based on the yrolysis interface model, a simulating aroach for charring ablation has been designed in order to obtain one dimensional transient thermal behavior of homogeneous charring materials in reentry casules. As the numerical results indicate, the yrolysis rate and the surface temerature under a given heat flux rise abrutly in the beginning, then reach a lateau, but the temerature at the bottom rises very slowly to revent the structural materials from being heated seriously. Pyrolysis mechanism can lay an imortant role in thermal rotection systems subected to serious aerodynamic heat. Key words: yrolysis, yrolysis interface model, charring materials, thermal rotection system Introduction The erformance of the thermal rotection system (TPS) is critical, since mass reduction trades directly with increase in science ayload for a given reentry mass or reduction in launch vehicle cost by using a lighter entry system and a smaller launch vehicle [1]. Charring materials are used in TPS for reentry vehicles such as Aollo and Orion casules. TPS can oerate by absorbing heat through decomosition and reecting it via yrolysis gas inection back into the boundary layer of gas. Traditionally, the design of a TPS has heavily relied on ground test. Ablation and yrolysis of charring materials were investigated through an ablation test motor []. Besides, it is very imortant to understand the hysical and chemical behavior of the TPS subected to aerodynamic heat [3]. The yrolysis interface is moving, so this is a moving boundary roblem. Some researchers analysed the temerature distribution, the mass loss rate and the surface recession through simulation [4-6]. Huang et al. [7] used the central difference scheme to solve moving boundary roblem in the one-dimensional thermal resonse. However, there were a few discussions on the thermal resonse and the moving rate of yrolysis interface in charring materials. This study will mainly focus on calculating the thermal resonse of olyester henolic comosites based on the yrolysis interface model. Pyrolysis interface model and numerical aroach The temerature gradient vertical to the surface is much higher than that in the other orientation, so the 1-D yrolysis interface model in fig. 1 can be built on the base of the * Corresonding author; hmhuang@btu.edu.cn

2 159 THERMA SCIENCE, Year 14, Vol. 18, No. 5, X c x q Char layer Virgin Surface Pyrolysis interface Figure 1. The yrolysis interface model following assumtions: (1) yrolytic reaction only occurs on the yrolysis interface that the yrolysis layer between a char layer and a virgin materials layer, and () yrolysis gases do not react chemically with the orous char layer through which it flows. From the model, we know that the surface temerature rises u to the yrolysis temerature T during -t s, and materials start to decomose. Then the yrolysis interface moves to the interior and a orous char layer aears, while yrolysis gas flows through the char layer and inects back into the boundary layer of gas. After a char layer comes into being (heating time > t s), the surface temerature is more than T and there are two layers which are a char layer and a virgin materials layer. Based on the Fourier s law of heat conduction, the heat conduction equations of the two layers are, resectively, deduced as: T( x, t) ρ11 c = k1 + m c x Xc (1) T( x, t) ρc = k Xc x () The boundary conditions are given in the form: T(,) x t k1 = q x= (3) T( x, t) = T x = X (4) k = x= (5) where ρ, c, and k are the density, secific heat caacity, and thermal conductivity, resectively, the subscrits 1 and are a char layer and a virgin materials layer, resectively; m is the mass flow rate of yrolysis; c the secific heat caacity of yrolysis gas. Pyrolysis mass rates are determined by the energy balance equation on a yrolysis interface, which is reresented by the relation: k1 = k + m h x= Xc (6) m = ( ρ ρ ) X (7) 1 where h is the latent heat in yrolysis and X c is the moving rate of yrolysis interface. In addition, there is only a virgin materials layer (X c = ) before char layer arises. The surface temerature is less than T in this eriod. The heat conduction equation is: c c T( x, t) ρc = k x (8)

3 THERMA SCIENCE, Year 14, Vol. 18, No. 5, The boundary conditions are: k = q x= k = x= (9) (1) The initial condition is given by: T( x,) = T (11) The heat conduction equations are obviously transient so that we have to discrete sace domain and time domain, resectively. Here we use the central difference format for sace domain and imlicit format for time domain as: T T = n n + 1 T 1 x n n n x t T+ 1 T + T 1 = (, ) T = n ( x) T t n 1 (1) (13) (14) We ut eqs. (1), (13), and (14) into eq. (1) and then let: k t mc t r = = ρ c c x so that the discrete equation can be deduced as: 1, z 1 1( x) ρ1 1 where n n 1 n n n n n = r + z T T T T T T T t ( x) x n 1 et A= 1+ r, B= r+ z, C = r z, and D= T, eq. (15) can be written as: T n B CQ + D = + A CP A CP n 1 T B CQ + D P = = A CP A CP 1, Q 1 1 (15) (16) The yrolysis interface is moving with the heating. In order to use Thomas algorithm to calculate the discrete equation, we introduce the method which fixes the time ste while changing sace ste to get the moving rate of yrolysis interface. The energy balance eq. (6) becomes:

4 1594 THERMA SCIENCE, Year 14, Vol. 18, No. 5, T n n n n + 1 T T + 1 T c 1 ( ρ ρ1) X k = k + h x x t From eq. (17), we can get the new moving distance X c of a yrolysis interface with every fixing time ste: n n n n T+ 1 T T+ 1 T k k1 t x x X c = ( ρ ρ ) h 1 Based on the above mathematical models and the iterative aroach, we can write a comuter code to calculate the thermal resonse. Results Taking a olyester henolic comosite as an examle, we can study one dimensional transient thermal behavior of homogeneous charring materials by means of the written comuter codes. The temerature T on the yrolysis interface is taken as 873 K, the latent Table 1. Physical arameters ρ [kgm 3 ] c [Jkg 1 K 1 ] k [Wm 1 K 1 ] Char layer [mm] Virgin materials Pyrolysis gas 366 (17) (18) heat h in the yrolysis is 31.5 MJ/kg, and the initial temerature T is 3 K. The hysical arameters of materials and yrolysis gas are given in tab. 1. From the arameters, we have obtained the thermal resonse of charring materials under the aerodynamic heat flux q = 879 W/m. Figure indicates the changes in surface temerature with heating time. The surface temerature rises raidly to the yrolysis temerature in the reliminary time, and then kees rising steadily, u to 94. K at 1 s. The interior temerature distributions at 1 s, s, 5 s, and 1 s is shown in fig. 3. The interior temerature distribution consists of two arts corresonding to the two layers. In initial heating time, the temerature distributions far away from yrolysis interface in virgin layer are T, comaring to which are of enormous rising gradient adacent to the yrolysis interface, which can be viewed on dot line. Heating continues and the char layer exands, while the virgin materials layer diminishes, which can be found in the other curves. The temerature gradient of the virgin is greater than that of the char layer, for the reason that the thermal conductivity of the two layers is.47 W/mK and 61.7 W/mK, resectively. The moving rate of yrolysis interface changing with the heating can be seen in fig. 4. In the initial heating time, the rate begins to rise raidly from the yrolysis at the beginning.45 s to 35.7 s, then kees rising gradually. The moving linear rate of yrolysis interface rises only.4 mm/s during 1-1 s, which is almost a steady state. Figure 5 shows the temerature at the bottom changes with the heating. In the initial heating time, the temerature at the bottom barely rises and stays at the initial temerature 3 K. Then it gradually rises u to 36.5 K when the heating time is s. When it is 1 s heating on the surface, the temerature at the bottom rises to K. The temerature at the bottom rises slowly with the function of yrolysis to revent the structural materials from being heated seriously.

5 THERMA SCIENCE, Year 14, Vol. 18, No. 5, Figure. Surface temeratures Figure 3. Interior temerature distributions Figure 4. Moving rate of yrolysis interface Figure 5. Bottom temerature Conclusions By simulating on the yrolysis of olyester henolic comosites on the base of the Fourier s law of heat conduction and the yrolysis mechanism, we have found the thermal resonse of charring materials under a heat flux. The results show that the moving rate of yrolysis interface and the surface temerature under a given heat flux rise abrutly in the beginning, then reaches a lateau, but the temerature at the bottom rises very slowly to revent the structural materials from being heated seriously. With the absorbing heat through decomosition and reecting it via yrolysis gas inection back into the boundary layer gas, charring materials can lay an imortant role in thermal rotection systems subected to severe aerodynamic heat. Acknowledgment This work is suorted by the National Natural Sciences Foundation of China (1174) and the China Manned Sace Engineering Office. Nomenclature c secific heat caacity, [Jkg 1 K 1 ] h latent heat, [MJkg 1 ] k thermal conductivity, [Wm 1 K 1 ] m mass flow rate, [kgm s 1 ] q heat flux on the surface, [Wm ] T temerature, [K] t heating time, [s] X c thickness of char layer, [mm] Subscrits 1 char layer virgin materials yrolysis Greeks symbols ρ mass density, [kgm 3 ]

6 1596 THERMA SCIENCE, Year 14, Vol. 18, No. 5, References [1] Venkataathy, E., et al., Thermal Protection System Develoment, Testing, and Qualification for Atmosheric Probes and Samle Return Missions: Examles for Saturn, Titan and Stardust-Tye Samle Return, Advances in Sace Research, 44 (9), 1, [] Pulci, G., et al., Carbon-Phenolic Ablative Materials for Reentry Sace Vehicle, Comosites Part A, 41 (1), 1, [3] Gokcen, T., et al., Comutational Analysis of Arcet Stagnation Tests Including Ablation and Shae Changed, Journal of Thermohysics and Heat Transfer, 4 (1), 4, [4] Huang, H. M., et al., The Inverse Problem in Zero inear Ablation of Aluminizing Carbon Comosites under High Heat Flux, Thermal Science, 17 (13), 5, [5] Ninković, D. P., Thermal and Aerodynamic Performances of the Suersonic Motion, Thermal Science, 14 (1), 4, [6] Ogasawara, T., et al., Ablation Behavior of Sic Fiber/Carbon Matrix Comosites under Simulated Atmosheric Reentry Conditions, Comosites Part A, 4 (11), 3,. 1-8 [7] Huang, H. M., et al., Thermal Resonse of Heat-resistant ayer with Pyrolysis, Thermal Science, 16 (1), 1, Paer submitted: February 1, 14 Paer revised: Aril 8, 14 Paer acceted: June 9, 14